Related papers: The Romance of the Ising Model
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
The ground state critical properties of the Random Field Ising Model (RFIM) on the diamond hierarchical lattice are investigated via a combining method encompassing real space renormalization group and an exact recurrence procedure. The…
The Random-Field Ising Model (RFIM) has been extensively studied as a model system for understanding the effects of disorder in magnets. Since the late 1970s, there has been a particular focus on realizations of the RFIM in site-diluted…
The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma…
This note presents an elementary proof of Hilbert's 1891 Ansatz of nesting for $M$-sextics, along the line of Riemann's Nachlass 1857 and a simple Harnack-style argument (1876). Our proof seems to have escaped the attention of Hilbert (and…
Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…
The statistical properties of pairwise majority voting over S alternatives is analyzed in an infinite random population. We first compute the probability that the majority is transitive (i.e. that if it prefers A to B to C, then it prefers…
A common issue when analyzing real-world complex systems is that the interactions between the elements often change over time: this makes it difficult to find optimal models that describe this evolution and that can be estimated from data,…
In the early fifties, the Belgian Prof. J. de Heinzelin discovered a bone in the region of a fishermen village called Ishango, at one of the farthest sources of the Nile, on the border of Congo and Uganda. The Heinzelin's Ishango bone has…
We present the discrete, q-, form of the Painlev\'e VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P_{VI} at the continuous limit and degenerates towards the…
The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable…
Given a curve $\Gamma$ and a set $\Lambda$ in the plane, the concept of the Heisenberg uniqueness pair $(\Gamma, \Lambda)$ was first introduced by Hedenmalm and Motes-Rodr\'{\i}gez (Ann. of Math. 173(2),1507-1527, 2011, \cite{HM}) as a…
We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical square, triangular and honeycomb lattice at the critical temperature. Fisher…
The discovery of the Higgs boson by the ATLAS and CMS experiments concluded a glorious century of experimental particle physics discoveries, from Rutherford's discovery of the nucleus in 1911, through the discoveries of quarks and leptons…
The transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature $\beta_{\mathrm{c}}$, which is determined by the…
A series of formula is presented that are all inspired by the Ramanujan Notebooks [6]. One of them appears in the notebooks II about Zeta(3). That formula inspired others that appeared in 1998, 2006 and 2009 on the author's website and…
The dynamics of a random (quenched) field Ising model (in two dimension) at zero temperature in the presence of an additional sinusoidally oscillating homogeneous (in space) magnetic field has been studied by Monte Carlo simulation using…
We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several…
We investigate the aging properties of phase-separation kinetics following quenches from $T=\infty$ to a finite temperature below $T_c$ of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range…
A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…